SOLUTION: 2 _______ 3-i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: 2 _______ 3-i      Log On


   

Question 207791: 2
_______
3-i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%29%2F%283-i%29 Start with the given expression.


%28%282%29%2F%283-i%29%29%28%283%2Bi%29%2F%283%2Bi%29%29 Multiply the fraction by %283%2Bi%29%2F%283%2Bi%29.


%28%282%29%283%2Bi%29%29%2F%28%283-i%29%283%2Bi%29%29 Combine the fractions.


%28%282%29%283%29%2B%282%29%28i%29%29%2F%28%283-i%29%283%2Bi%29%29 Distribute


FOIL the denominator.


%286%2B2i%29%2F%289%2B3i-3i-i%5E2%29 Multiply.


%286%2B2i%29%2F%289%2B3i-3i-%28-1%29%29 Replace i%5E2 with -1


%286%2B2i%29%2F%289%2B3i-3i%2B1%29 Simplify


%286%2B2i%29%2F%2810%29 Combine like terms.


%286%29%2F%2810%29%2B%28%282%29%2F%2810%29%29i Break up the fraction.


3%2F5%2B%281%2F5%29i Reduce.


So %282%29%2F%283-i%29=3%2F5%2B%281%2F5%29i.


So the expression is now in standard form a%2Bbi where a=3%2F5 and b=1%2F5